I live in Florence. I’m actually surprised you thought there were too many people in August - the city is empty because locals went to vacation, and is actually low season for hotels because many countries in Europe start schools around the 15th. I was walking last night downtown and I was impressed how empty it was :)
At the same time, weather in August is better than July and June on average — you usually get some storms and thus some relief from hot. But yes, it’s still hottish but that’s Italy.
It’s true that the best seasons would be Spring and Fall. But you get many many more tourists, longer queues, and much higher prices for hotels. So YMMV.
Spring and Fall are often the best seasons to visit Italy. Among other things, a lot of Italians go on vacation themselves in August, meaning fewer stores and things are open.